CN104393963A - Space time block coding (STBC) MC-CDMA (Multicarrier Code Division Multiple Access) signal blind identification method based on cyclostationarity - Google Patents

Abstract

The invention claims to protect a space time block coding (STBC) MC-CDMA (Multicarrier Code Division Multiple Access) signal blind identification method based on the cyclostationarity, and belongs to the technical field of signal processing. The method comprises the following steps: establishing a selection standard of signal correlation functions according to the baseband physical model, signal construction and matrix representation of an STBC MC-CDMA system, and estimating corresponding fourth-order cumulants of the correlation functions; combining a fourth-order cyclic cumulant with the parameter of a channel to establish a cyclic statistic; and extracting a detection threshold according to the detection of cycle frequency, and making a judgment by comparing the detection threshold with the cyclic statistic to realize identification. As indicated by computer simulation, STBCMC-CDMA signals can be effectively identified with low complexity by adopting an algorithm adopted in the invention, and working under the condition of low input signal to noise ratio is feasible. Meanwhile, compared with a conventional identification algorithm, the algorithm adopted in the invention has the advantage that the influence of random noise is reduced by using the advantage of the fourth-order cyclic cumulant, so that the system performance is improved.

Description

Based on the Space-Time Block Coding MC-CDMA Signal blind recognition method of cyclostationarity

Technical field

The present invention relates to signal processing technology field, more specifically Signal blind recognition method.

Background technology

MC-CDMA (MC-CDMA, Multicarrier Code Division Multiple Access) technology is OFDM (OFDM, Orthogonal Frequency Division Multiplexing) with the combination of code division multiple access (CDMA), there is the major advantage of two kinds of technology.In broadband system, MC-CDMA system is converted to the flat fading channel of a series of experience arrowband the frequency-selective channel in broadband.The shortcoming of receive diversity is that the calculated load of receiving terminal is very high, and the power consumption of the travelling carriage in down link may be caused very large.Transmitting terminal uses Space Time Coding can obtain diversity gain equally, and only needs simple linear process when receiving terminal is decoded.Space-time code organically combines antenna transmission diversity technology, chnnel coding and modulation technique, effectively can improve the transmission performance of fading channel.Space-time code and MC-CDMA are combined, a broadband system can be made to obtain transmit diversity.Space-time code is the one coding to sending symbol in mimo system, and the identification of space-time code is one of important content of non-cooperation mimo system.

Cyclic cumulants can be relatively accurate the random Digital and analog signal of communication of description, the theory of cyclic cumulants has caused the concern of height.When signal and noise circumstance are difficult to supposition, usually use the cyclostationarity of signal.Due to the correlation in Space-Time Block Coding life period, and BLAST does not exist.According to this character, realize STBC MC-CDMA by circulation Higher-order Cumulants and identify.

Summary of the invention

Space Time Coding Application comparison is sky layered code (BLAST widely, Bell Labs Layered Space Time) and Space-Time Block Coding (STBC, Space Time Block Coding), technical problem to be solved by this invention is, how have employed which kind of Space Time Coding in receiving terminal determination multiaerial system.For the multi-input multi-ouput channel using multiple antennas, the present invention proposes a kind of circulation Higher Order Cumulants that utilizes and adds up the method identifying Space-Time Block Coding.

The technical scheme that the present invention solves the problem is as follows:

Based on the Space-Time Block Coding MC-CDMA Signal blind recognition method of cyclostationarity, analyze based on the cyclostationarity of Space-Time Block Coding MC-CDMA signal, first set up the choice criteria of signal correction function, estimate the fourth order cumulant that these correlation functions are corresponding, then follow the parameter of channel to combine fourth order cumulant and set up a Cyclic Statistics, finally follow this Cyclic Statistics to compare according to the Detection and Extraction detection threshold of cycle frequency and do judgement realization identification.

Concrete steps are as follows:

Step one: by signal Y(t) by T _ssampling formation time series, extract the code check of signal, obtain the correlation function number R of signal according to formula (29):

$\begin{array}{c}f\left(t\right)=E\left\{g\right[y_i(2t-1)y_j\left(2t\right)\left]\right\}\mathrm{orE}\left\{g\right[y_i(2t-1)y_j^{*}\left(2t\right)\left]\right\}\\ =f(t+\mathrm{lp})\end{array}---\left(29\right)$

T is the numbering of space-time code block, t=1,2 ..., LT, l are positive numbers, and f (t) is the function of period p, and g [] is a linear correlation function, definition $g[\&CenterDot;]=y_i(2t-1)y_i\left(2t\right)\mathrm{or}{y}_i(2t-1)y_j^{*}\left(2t\right),$ 0≤i, j ∈ I < M, I is set of integers;

Step 2: at cycle frequency α=± T/2T _s, the fourth-order cumulant value of respective signal is calculated according to formula (28)

${\hat{C}}_{4Y}(\mathrm{\&alpha;},\mathrm{\&tau;})=\frac{1}{N}\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}Y\left(n\right)Y^{*}(n+p)Y\left(n\right)Y^{*}(n+p).\exp (-\mathrm{j\&alpha;t})---\left(28\right);$

Step 3: the phase estimating the stable circulation first peak of corresponding each correlation function according to formula (33) ^r

$\mathrm{\&phi;}=\mathrm{angle}\left\{\frac{1}{T}\underset{k=0}{\overset{T-1}{\mathrm{\&Sigma;}}}E\right\{g\left[y_i(2t-1)y_i\left(2t\right)\right]\}.\exp [-\frac{j2\mathrm{\&pi;t}}{T}\left]\right\}---\left(33\right);$

Step 4: according to hypothesis detect with converging on zero-mean variance asymptotic is ∑ _acthis character of multivariate normal distributions estimate a circle statistics value th _ac, adopt formula (31) or formula (34) to estimate:

${\mathrm{th}}_{\mathrm{ac}}=N{\hat{c}}_{\mathrm{aY}}(t;\mathrm{\&tau;}){\widehat{\mathrm{\&Sigma;}}}_{\mathrm{ac}}^{-1}{\hat{c}}_{\mathrm{aY}}{(t;\mathrm{\&tau;})}^T---\left(31\right)$

In formula, N is data length, be the estimation of covariance matrix

${\mathrm{th}}_{\mathrm{ac}}=\underset{r=0}{\overset{R-1}{\mathrm{\&Sigma;}}}{\left|\exp (-j2\mathrm{\&pi;}{\mathrm{\&phi;}}^r){\hat{C}}_{4Y}^r\left(\mathrm{\&alpha;}\right)\right|}^2---\left(34\right)$

In formula, R is the relative number of classifying by standard (29);

Step 5: according to the formula (27) of cycle frequency, obtain detection threshold value γ by formula (35)

Wherein A ₄it is the cycle frequency set of quadravalence cyclic cumulants;

p _F＝p(χ ²＞γ) (35)

P _fit is false alarm probability;

Step 6: compare judgement, if namely th>=γ illustrates hypothesis H ₁set up, namely have employed STBC signal; Otherwise, otherwise H ₀set up, namely have employed BLAST signal.

From above technical scheme, the first baseband physical model according to system in space-time block code MC-CDMA of the present invention, signal configuration and matrix notation, due to the correlation in Space-Time Block Coding life period, and there is not this correlation in time in BLAST, so Space-Time Block Coding exists a peculiar cycle frequency on higher-order determinant, and BLAST does not exist.According to this character, the present invention establishes the choice criteria of signal correction function, and then these correlation functions and channel parameter are combined, and compares judgement, from then on improve the effect of identification by the Cyclic Statistics estimated with detection threshold.

Computer simulation shows, the algorithm that the present invention adopts can identify STBC MC-CDMA signal effectively with less complexity, and can work well under lower input signal-to-noise ratio condition., compare with traditional recognizer, the algorithm that the present invention adopts utilizes the advantage of quadravalence cyclic cumulants to reduce the impact of random noise, thus improves systematic function meanwhile.

Accompanying drawing explanation

Fig. 1 STBC MC-CDMA transmitting terminal block diagram,

The fourth order cumulant block diagram of Fig. 2 signal, the fourth order cumulant of (a) STBC signal, the fourth order cumulant of (b) BLAST signal, the fourth order cumulant of (c) STBC signal, the fourth order cumulant Quadratic Spectrum of (d) STBC signal;

Fig. 3 discrimination curve block diagram, discrimination under (a) different channels environment, discrimination under (b) different rates signal environment, (e) adopts different correlation algorithm discrimination, the error rate of (f) channel parameter estimation;

Fig. 4 algorithm flow block diagram of the present invention.

Embodiment

Consider that number of users is the synchronous STBC MC-CDMA system up-link of K, kth user's base band Space-Time Block Coding MC-CDMA transmitter as shown in Figure 1, mobile terminal has M=2 transmitting antenna, base station single receive antenna, use two different spreading codes corresponding to two each users of transmitting antenna, suppose that sub-carrier number is equal with spreading factor.Make d ^(k)t information symbol sequence that () sends for user k, adopts the time block coding scheme of Alamouti, moment 2t-1 and 2t (t is the numbering of space-time code block, t=1,2 ..., LT) two symbol d ^(k)(2t-1) and d ^(k)(2t) be input to space-time encoders, export following code matrix:

$\begin{array}{c}{S}^{\left(k\right)}\left(t\right)=\left[\begin{array}{cc}{S_1}^{\left(k\right)}(2t-1)& {S_1}^{\left(k\right)}\left(2t\right)\\ {S_2}^{\left(k\right)}(2t-1)& {S_2}^{\left(k\right)}\left(2t\right)\end{array}\right]\\ =\left[\begin{array}{cc}{d}^{\left(k\right)}(2t-1)& -d^{\left(k\right)*}\left(2t\right)\\ d^{\left(k\right)}\left(2t\right)& d^{\left(k\right)*}(2t-1)\end{array}\right]\end{array}---\left(1\right)$

In above formula, S ^(k)t two row of () are launched at moment 2t-1 and 2t respectively, the one-component often arranged is from first antenna transmission, and second component is from second antenna transmission.Wherein, ${w_1}^{\left(k\right)}={[{w_1}^{\left(k\right)}{w_1}^{\left(k\right)}\left(2\right),...,{w_1}^{\left(k\right)}\left(Q\right)]}^T$ For the spreading code of user k first transmitting antenna, (q=1,2 ... Q), Q is spreading factor.The signal of information symbol after spread spectrum of first transmitting antenna is: it is f that each chip (chip) of spreading code is modulated to centre frequency _qsubcarrier on.

OFDM modulation can realize with inverse Discrete Fourier transform (IDFT), namely

In formula, for the IDFT matrix of Q × Q dimension, the component of the capable q row of its q is x ₁ ^(k)t () is called an OFDM symbol.In like manner, the signal x of second transmitting antenna can be obtained ₂ ^(k)(t).Signal from before antenna transmission, at x ₁ ^(k)(t) and x ₂ ^(k)t () above intubating length is greater than the Xun Huan Qian Suffix protection interval of channel impulse response length, in order to eliminate the impact of intersymbol interference (ISI).

In receivers; Received signal strength becomes Parallel Sequence through serial/parallel conversion; remove the protection interval of Cyclic Prefix; suppose to protect the length at interval to be longer than the length of channel impulse response; then there is not ISI and code inter-block-interference (IBI); after discrete Fourier transform (DFT), the data vector corresponding to two continuous symbol time intervals of t space-time code block can be expressed as each user of continued time domain in the data of every root antenna to represent with following formula:

$\left\{\begin{array}{c}y(2t-1)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\sqrt{E^{\left(k\right)}}({W_1}^{\left(k\right)}{b_1}^{\left(k\right)}{d}^{\left(k\right)}(2t-1)+{W_2}^{\left(k\right)}{b_2}^{\left(k\right)}{d}^{\left(k\right)}\left(2t\right))+v(2t-1)\\ y\left(2t\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\sqrt{E^{\left(k\right)}}(-{W_1}^{\left(k\right)}{b_1}^{\left(k\right)}{d}^{\left(k\right)*}\left(2t\right)+{W_2}^{\left(k\right)}{b_2}^{\left(k\right)}{d}^{\left(k\right)*}(2t-1))+v\left(2t\right)\end{array}\right.---\left(3\right)$

Wherein E ^(k)for the signal power of user k; Diagonal matrix is $W_m^{\left(k\right)}=\mathrm{diag}\{w_m^{\left(k\right)}\left(1\right),...,w_m^{\left(k\right)}\left(Q\right)\},m=\mathrm{1,2},$ Its diagonal entry is Q chip of user k m transmitting antenna spreading code; for from kth user m transmitting antenna to the channel impulse response of reception antenna, $h_m^{\left(k\right)}={[h_m^{\left(k\right)}\left(1\right),...,h_m^{\left(k\right)}\left(L\right)]}^T$ Q point discrete Fourier in leaf transformation, $b_m^{\left(k\right)}=F{h}_m^{\left(k\right)},$ F is the Discrete Fourier transform of Q × L dimension, supposes distinguishable number of path L<<Q; V (t) is for tieing up additive white Gaussian noise vector in Q × 1, and its average is zero, correlation matrix R _v=E [v (t) v ^h(t)]=σ ²i, σ ²=N ₀/ 2, N ₀/ 2 is bilateral power spectral densities, I representation unit matrix.

Structure Q × 1 n dimensional vector n Y (t)=[y ^t(2t-1), y ^h(2t)], n (t)=[v ^t(2t-1), v ^h(2t)] ^t, then Y (t) can be expressed as

$Y\left(t\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\sqrt{E^{\left(k\right)}}(x_o^{\left(k\right)}{h}^{\left(k\right)}\left(1\right)+x_e^{\left(k\right)}{h}^{\left(k\right)}\left(2\right))+n\left(t\right)$

$=\mathrm{XH}+n\left(t\right)---\left(4\right)$

$x_o^{\left(k\right)}{=A_o^{\left(k\right)}d}^{\left(k\right)}\left(t\right),x_e^{\left(k\right)}=A_e^{\left(k\right)}{d}^{\left(k\right)}\left(t\right)---\left(5\right)$

$\left\{\begin{array}{c}{A}_o^{\left(k\right)}=\left[\begin{array}{cc}{W}_1^{\left(k\right)}& 0\\ 0& W_2^{\left(k\right)*}\end{array}\right]\left[\begin{array}{cc}F& 0\\ 0& F\end{array}\right]\\ A_e^{\left(k\right)}=\left[\begin{array}{cc}0& W_2^{\left(k\right)}\\ -W_1^{\left(k\right)*}& 0\end{array}\right]\left[\begin{array}{cc}F& 0\\ 0& F\end{array}\right]\end{array}\right.---\left(6\right)$

Wherein 0 represents that all elements is all the null matrix of zero, $=[A_o^{\left(1\right)},A_e^{\left(1\right)},...,A_o^{\left(K\right)},A_e^{\left(k\right)}]$ For 2Q × 4LK ties up matrix, $h\left(k\right)={[h_1^{\left(k\right)T},h_2^{\left(k\right)T}]}^T$ For a kth subscriber channel coefficient vector, for h ⁽¹⁾, h ⁽¹⁾..., h ^(K), h ^(K)the block diagonal matrix of composition, for 2Q × 2K ties up matrix, d (t)=[d ⁽¹⁾(2t-1), d ⁽¹⁾(2t) ..., d ^(K)(2t-1), d ^(K)(2t)] ^t.In order to ensure that A is the matrix of full column rank, supposing K < 2Q/4L, as K > 2Q/4L, can solve by adopting array antenna technique.Construct the 2Q × T be made up of the data vector corresponding to T code block and tie up matrix

Y＝[Y(1)，Y(2)，...，Y(T)]

Y＝XH+N (7)

X=in above formula [X (1) ..., X (T)] be that 2K × T ties up matrix, N=[n (1) ..., n (T)] be that 2Q × T ties up matrix.

Space Time Coding Application comparison is sky layered code and Space-Time Block Coding widely, and how have employed which kind of Space Time Coding in receiving terminal determination multiaerial system becomes the problem that must study.For the multi-input multi-ouput channel using multiple antennas.Based on analysis above, the utilization circulation Higher Order Cumulants statistics that the present invention proposes identifies the method for Space-Time Block Coding.

Greatest hope (Epectation Maximization) algorithm is used for processing the X factor affecting Output rusults, is now widely used in every field, as signal transacting, science of heredity, econometrics, clinical and sociological research.Channel estimating based on EM is a kind of iterative technique, estimates for finding the maximum likelihood (ML) of channel.Due to cannot obtain transmit time, can also channel estimating be realized, so be divided into semi-blind method based on the channel estimation technique of EM algorithm.Although EM algorithm has lot of advantages, it can not directly apply to the channel estimating of STBC MC-CDMA system, because the computation complexity of EM algorithm exponentially raises with the increase of transmit quantity or constellation point quantity.In addition, EM algorithm can not be used for time varying channel.EM algorithm and decision directed channel estimation combine by decision-feedback EM (DEM) estimation technique, reduce the computation complexity for slow time-varying channel.

Suppose that channel H is constant in D STBC MC-CDMA symbol period, the Received signal strength on so a certain subcarrier can be expressed as Y=HX+N, also can represent these transmitting and receiving symbols Y=[Y by vector form ¹, Y ²..., Y ^d],

${\tilde{X}}^d={\widehat{\mathrm{\&Delta;}}}^d<\&CenterDot;>{\hat{X}}^d={[{\widehat{\mathrm{\&alpha;}}}_1^d{\hat{X}}_1^d,{\widehat{\mathrm{\&alpha;}}}_2^d{\hat{X}}_2^d,...,{\widehat{\mathrm{\&alpha;}}}_M^d{\hat{X}}_M^d]}^T---\left(8\right)$

The wherein coefficient of variation interpositioning or filtering technique can be adopted to estimate with lead code and training sequence, and symbol <> represents that element correspondence is multiplied.

Given with y ^dcondition PDF (Probability Density Function) can be expressed as

$f\left(Y^d\right|{\tilde{X}}^d,\hat{H})=\frac{1}{2\mathrm{\&pi;}{\mathrm{\&sigma;}}^{d2}\left(p\right)}\exp \{-\frac{1}{2{\mathrm{\&sigma;}}^{d2}\left(p\right)}{|Y^d-\hat{H}{\tilde{X}}^d|}^2\}---\left(9\right)$

In DEM algorithm, because the data X launched is hidden among observation data Y, so Y is called as the data of " imperfect ".In addition, the data that (Y, X) is called as " complete ", because it includes observation data and potential data Y.Because use the data of " imperfect " to be difficult to estimate channel, so need the PDF PDF of " imperfect " data being converted into " complete " data.The PDF of " imperfect " data is

$f\left(Y\right|\tilde{X},\hat{H})=\underset{d=1}{\overset{D}{\mathrm{\&Pi;}}}f\left(Y^d\right|{\tilde{X}}^d,\hat{H})---\left(10\right)$

Also with log-likelihood function, above formula can be expressed as

$\log f\left(Y\right|\tilde{X},\hat{H})=\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}\log f\left(Y^d\right|{\tilde{X}}^d,\hat{H})---\left(11\right)$

In traditional ML algorithm, by maximizing the likelihood function in formula (9) realize the estimation to H.But, because it is the sum term of exponential function, so be difficult to the closed solutions obtaining H.In DEM algorithm, increase the likelihood function in formula (11) by iterative manner, realize the estimation to H with this.In reality, EM algorithm is made up of two iterative steps: calculation expectation value (E step) and maximization (M step).In E step, the latest estimated value of given Y and H, calculates the desired value of log-likelihood function about X of H:

$\begin{array}{c}Q\left(H\right|H\left(p\right))=E\left[\log f(Y,X|H)\right|X,H\left(p\right)]\\ =\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}\log \left\{f\left(Y^d\right|{\tilde{X}}^d,H)\right\}f\left(Y^d\right|{\tilde{X}}^d,H\left(p\right))\end{array}---\left(12\right)$

Wherein, H (p) represents the latest estimated value of H.In E step, the log-likelihood function of " complete " data in formula (12) is averaged in D OFDM symbol.In M step subsequently, in all possible H, find and make formula (12) get the H of maximum as H (p+1), more specifically, ask formula (12) about H derivative and make derivative be zero, following result can be obtained:

$\begin{array}{c}\underset{H}{\arg \max }Q\left(H\right|H\left(p\right))\\ =\underset{H}{\arg \min }\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}|Y^d-H{\tilde{X}}^d{|}^{2}f\left(Y^d\right|{\tilde{X}}^d,H\left(p\right))\end{array}---\left(13\right)$

$\begin{array}{c}H(p+1)={\left[\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}{\tilde{X}}^d{\left({\tilde{X}}^d\right)}^{T}f\left(Y^d\right|{\tilde{X}}^d,H\left(p\right))\right]}^{-1}\\ \&times;\left[\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}{Y}^d{\left({\tilde{X}}^d\right)}^{T}f\left(Y^d\right|{\tilde{X}}^d,H\left(p\right))\right]\end{array}---\left(14\right)$

Can represent with lower formula at the noise of (p+1) secondary iteration

$\begin{array}{c}{\mathrm{\&sigma;}}^{d2}(p+1)=\frac{1}{p+1}({\mathrm{p\&sigma;}}^{d2}\left(p\right)+{\left(Y^d(p+1)\right)}^2)\\ {-2Y}^d(p+1)H(p+1){\stackrel{\stackrel{\&OverBar;}{~}}{X}}^d(p+1)\\ +H{(p+1)}^T\stackrel{\&OverBar;}{{\tilde{X}}^d(p+1){\tilde{X}}^d{(p+1)}^T}H(p+1)\end{array}---\left(15\right)$

In formula $\stackrel{\&OverBar;}{{\tilde{X}}^d(p+1){\tilde{X}}^d{(p+1)}^T}={E[\tilde{X}}^d(p+1){\tilde{X}}^d{(p+1)}^T|Y^d,\hat{H}].$ Under the condition of satisfied expection, the estimation of last channel parameter values

${\hat{H}}^d=H(p+1)\&lang;\&CenterDot;\&rang;{\left({\widehat{\mathrm{\&Delta;}}}^d\right)}^T---\left(16\right)$

Adopt ML (Maximum Likelihood) technology with detection signal, then the estimation after input

${\hat{X}}^d=\underset{{\hat{X}}^d\&Element;\mathrm{\&Omega;}}{\arg \min }\left({\left|\right|Y^d-{\hat{H}}^d{\hat{X}}^d\left|\right|}^2\right)---\left(17\right)$

${\hat{X}}^d=\mathrm{Slice}({(\left({\hat{H}}^d\right)*{\hat{H}}^d)}^{-1}\left({\hat{H}}^d\right)*Y^d)---\left(18\right)$

Wherein Slice (), Ω represent slice function and the collection that transmits.If use LMS (Least Mean Square) algorithm, calculated by following formula in the channel parameter values of (p+1) secondary iteration

${\hat{H}}^d(p+1)={\hat{H}}^d\left(p\right)+2\mathrm{\&mu;}{\mathrm{\&epsiv;}}^d\left(p\right){\tilde{X}}^d\left(p\right)---\left(19\right)$

The p time iteration error code can with under formula represent

ε ^d(p)＝Y ^d(p)-H(p) ^TX ^d(p) (20)

The LS (Least Square) that attention formula (14) can regard a weighting as separates, wherein with the cross-correlation function estimated divided by the white correlation function estimated, and with each correlation function of corresponding PDF weighting.

When data available is imperfect, DEM algorithm is useful especially channel estimation methods.When input signal cannot obtain or be insufficient, incomplete data may go wrong.Such as, in a STBC MC-CDMA system, need to utilize the channel condition information between transmitting antenna and reception antenna to carry out relevant decoding.But, because the Received signal strength of each MC-CDMA subcarrier is the superposition from different transmit antennas, traditional channel estimation technique can not be used.The estimation problem of a multi input channel can be converted into the estimation problem of some single input channels by DEM algorithm.In addition, the MS (Mobile Station) being positioned at cell edge can be subject to presence of intercell interference, and now DEM algorithm will be very useful channel estimation methods.In this case, the superposed signal that what MS received is from adjacent base station (BS, Base Station), and be unknown for MS.As long as channel is constant when in D symbol period being, by using DEM algorithm just can improve the performance of cell edge to the extra data received.DEM algorithm realization step is as follows:

Step one: each parameter of initialization, calculates

Step 2: calculate signal by formula (17) and (18)

Step 3: calculate (p+1) secondary iterative channel value H (p+1) by formula (14)

Step 4: calculate (p+1) secondary iteration noise level σ by formula (15) ^d2(p+1)

Step 5: when meeting anticipated conditions, finishing iteration, calculates last channel value by formula (16) otherwise, return step 2.

Due to the correlation in Space-Time Block Coding life period, and there is not this correlation in BLAST in time, so Space-Time Block Coding exists a peculiar cycle frequency on higher-order determinant, BLAST does not exist.According to this character, carry out Space-Time Block Coding MC-CDMA identification by circulation Higher Order Cumulants.Cyclic cumulants can be relatively accurate the random Digital and analog signal of communication of description, the theory of cyclic cumulants has caused the concern of height.When signal and noise circumstance are difficult to supposition, usually use the cyclostationarity of signal, cyclic cumulants is the statistic of one-period change, and the stable circulation characteristic certainly existing a rank meets periodically.The a rank square m of signal Y (t) _aY(t; τ)

m _aY(t；τ)＝E{Y(t)Y ^*(t+τ ₁)...Y ^*(t+τ _a-1)} (21)

To m _aY(t; τ) do rich in leaf transformation obtain circulation a rank square M _aY

$M_{\mathrm{aY}}=\underset{N\&RightArrow;\&infin;}{\lim }\underset{t=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{m}_{\mathrm{aY}}(t;\mathrm{\&tau;})\exp (-\mathrm{j\&alpha;t})---\left(22\right)$

In formula, a is cycle frequency.Same a rank cumulant c _aYwith Cyclic Autocorrelation Function C _aY(α; τ) be

$\left\{\begin{array}{c}{c}_{\mathrm{aY}}(t;\mathrm{\&tau;})=\underset{\mathrm{\&alpha;}}{\mathrm{\&Sigma;}}{C}_{\mathrm{aY}}(\mathrm{\&alpha;};\mathrm{\&tau;})\exp \left(\mathrm{j\&alpha;t}\right)\\ C_{\mathrm{aY}}(\mathrm{\&alpha;};\mathrm{\&tau;})=\underset{T\&RightArrow;\&infin;}{\lim }\frac{1}{T}\underset{t=0}{\overset{T-1}{\mathrm{\&Sigma;}}}{c}_{\mathrm{aY}}(t;\mathrm{\&tau;})\exp (-\mathrm{j\&alpha;t})\end{array}\right.---\left(23\right)$

Formula is called correlation function second moment in (23), and because second moment is equal separately in the different moment with third moment, so when cycle frequency α=0, Cyclic Moment and Cyclic Autocorrelation Function be not also equal separately in the same time.

Quadravalence Cyclic Autocorrelation Function defines

$\begin{array}{c}{C}_{4Y}(\mathrm{\&alpha;};{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&tau;}}_3)=M_{4Y}(\mathrm{\&alpha;};{\mathrm{\&tau;}}_1,{\mathrm{\&tau;}}_2,{\mathrm{\&tau;}}_3)-\\ -\underset{\mathrm{\&beta;}\&Element;A_2^m}{\mathrm{\&Sigma;}}\left(\begin{array}{c}{M}_{2Y}(\mathrm{\&alpha;}-\mathrm{\&beta;};{\mathrm{\&tau;}}_1)M_{2Y}(\mathrm{\&beta;};{\mathrm{\&tau;}}_1)\exp \left(j{\mathrm{\&beta;\&tau;}}_2\right)+\\ +M_{2Y}(\mathrm{\&alpha;}-\mathrm{\&beta;};{\mathrm{\&tau;}}_2)M_{2Y}(\mathrm{\&beta;};{\mathrm{\&tau;}}_1-{\mathrm{\&tau;}}_3)\exp \left(\mathrm{j\&beta;}{\mathrm{\&tau;}}_3\right)+\\ +M_{2Y}(\mathrm{\&alpha;}-\mathrm{\&beta;};{\mathrm{\&tau;}}_3)M_{2Y}(\mathrm{\&beta;};{\mathrm{\&tau;}}_2-{\mathrm{\&tau;}}_1)\exp \left(\mathrm{j\&beta;}{\mathrm{\&tau;}}_1\right)\end{array}\right)\end{array}---\left(24\right)$

In formula the set of second-order cyclic frequency, so the part of second-order cyclic square is 0 in Section 2 and formula, obtain following formula

C _4Y(α；τ ₁，τ ₂，τ ₃)＝M _4Y(α；τ ₁，τ ₂，τ ₃) (25)

When adopting quadravalence cyclic cumulants, a cycle frequency α=± T/2T be it is expected to Space-Time Block Coding _s, 1/T _sfor code check, 1/T is sample rate.When Space-Time Block Coding adopts the cyclic cumulants of more high-order, cycle frequency is different altogether.Such as 4 × 4 quasi-orthogonal space time block code when employing 8 rank cyclic cumulants, cycle frequency α=± T/4T _s.

Owing to needing to detect cycle frequency in testing process, and cycle frequency is relevant with the code check of signal, so determine that the code check of signal is necessary.Suppose that the code check of signal is known, then detect cycle frequency α=± T/2T _sexistence, if there is cycle frequency α, illustrate and have employed STBC; Otherwise, have employed BLAST signal.

By sampling, the quadravalence cyclic cumulants obtained equals real quadravalence cyclic cumulants and error sum

${\hat{C}}_{4Y}(t;\mathrm{\&tau;})=C_{4Y}(t;\mathrm{\&tau;})+{\mathrm{\&epsiv;}}_{4Y}^T(\mathrm{\&alpha;};\mathrm{\&tau;})---\left(26\right)$

Wherein for evaluated error, T is data length.The method that hypothesis can be utilized under the guide of this formula to detect is right to carry out the detection of cycle frequency.Definition ${\hat{c}}_{4Y}(t;\mathrm{\&tau;})=\left\{\mathrm{Re}\right\{{\hat{C}}_{4Y}(t;\mathrm{\&tau;})\},\mathrm{Im}\{{\hat{C}}_{4Y}(t;\mathrm{\&tau;})\left\}\right\},$ Same c _4Y(t; τ)={ Re{C _4Y(t; τ) }, Im{C _4Y(t; τ) } }, the hypothesis then provided below detects

Wherein A ₄it is the cycle frequency set of quadravalence cyclic cumulants.

${\hat{C}}_{4Y}(\mathrm{\&alpha;},\mathrm{\&tau;})=\frac{1}{N}\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}Y\left(n\right)Y^{*}(n+p)Y\left(n\right)Y^{*}(n+p).\exp (-\mathrm{j\&alpha;t})---\left(28\right)$

For STBC signal, because the correlation function of not all signal can produce a stable circulation sequence, so a standard selecting correlation function must be had.We can be the center χ of n in order to the degree of freedom ²correlation function is selected in distribution.

Represent with following formula from formula (27) standard to select correlation function to have

$\begin{array}{c}f\left(t\right)=E\left\{g\right[y_i(2t-1)y_i\left(2t\right)\left]\right\}\mathrm{orE}\left\{g\right[y_i(2t-1)y_j^{*}\left(2t\right)\left]\right\}\\ =f(t+\mathrm{lp})\end{array}---\left(29\right)$

L is positive number, and f (t) is the function of period p, and g [] is a linear correlation function, definition

$g[\&CenterDot;]=y_i(2t-1)y_i\left(2t\right)\mathrm{or}{y}_i(2t-1)y_j^{*}\left(2t\right),$ 0≤i, j ∈ I < M, I is set of integers.

When go by standard (29) select correlation function time, we can only in three kinds of situations to select suitable correlation function.Generally, we can use the emission matrix of STBC scheme to obtain the correlation function that some meet standard (29).Such as, as number of transmit antennas M=3, during data code block T=4, the selectable correlation function of 3/4 speed STBC is represented by table 1

Table 1 correlation function

Table 1 The Correlators

x 0x 0 H	x 0x 1 T	x 0x 2 T	x 0x 3 T
				x 1x 0 H	x 1x 1 H	x 1x 2 T	x 1x 3 T
x 2x 0 H	x 2x 1 H	x 2x 2 H	x 2x 3 T
				x 3x 0 H	x 3x 1 H	x 3x 2 H	x 3x 3 H

Wherein, x _i(t)=s _i(t) w, i=0,1 ..., T-1.Emission matrix becomes in formula (1)

$\left\{\begin{array}{c}{s}_0{=[d(2t-1),d\left(2t\right),d(2t+1)]}^T\\ s_1{=[-d^{*}\left(2t\right),d^{*}(2t-1),d(2t+1)/\sqrt{2}]}^T\\ s_2={[\frac{d^{*}(2t+1)}{\sqrt{2}},\frac{d^{*}(2t+1)}{\sqrt{2}},(-d(2t-1)-d^{*}(2t-1)+d\left(2t\right)-d^{*}\left(2t\right))]}^T\\ s_3={[\frac{d^{*}(2t+1)}{\sqrt{2}},\frac{-d^{*}(2t+1)}{\sqrt{2}},(d(2t-1)-d^{*}(2t-1)+d\left(2t\right)+d^{*}\left(2t\right))]}^T\end{array}\right.---\left(30\right)$

For BLAST signal, the correlation function of all signals all can not produce a stable circulation sequence.Although STBC and BLAST two kinds of signals can be detected by above standard, but if only often ensure the performance detected not by these correlation functions.So, these correlation functions and some parameters are combined, in order to go to set up detection threshold, from then on improves the performance of detection.

At known track data code block T under not knowing any other Parameter Conditions, converging on zero-mean variance asymptotic is ∑ _acmultivariate normal distributions.Cyclic Statistics according to this property definition

${\mathrm{th}}_{\mathrm{ac}}=N{\hat{c}}_{\mathrm{aY}}(t;\mathrm{\&tau;}){\widehat{\mathrm{\&Sigma;}}}_{\mathrm{ac}}^{-1}{\hat{c}}_{\mathrm{aY}}{(t;\mathrm{\&tau;})}^T---\left(31\right)$

In formula, N is data length, be the estimation of covariance matrix.

${\widehat{\mathrm{\&Sigma;}}}_{\mathrm{ac}}=\left[\begin{array}{cc}\mathrm{Re}\left\{\frac{{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}(2\mathrm{\&alpha;};\mathrm{\&alpha;})+{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}^{*}(0;-\mathrm{\&alpha;})}{2}\right\}& \mathrm{Im}\left\{\frac{{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}(2\mathrm{\&alpha;};\mathrm{\&alpha;})-{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}^{*}(0;-\mathrm{\&alpha;})}{2}\right\}\\ \mathrm{Im}\left\{\frac{{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}(2\mathrm{\&alpha;};\mathrm{\&alpha;})-{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}^{*}(0;-\mathrm{\&alpha;})}{2}\right\}& \mathrm{Re}\left\{\frac{{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}(2\mathrm{\&alpha;};\mathrm{\&alpha;})-{\hat{S}}_{{\mathrm{af}}_{\mathrm{\&tau;},\mathrm{\&tau;}}}^{*}(0;-\mathrm{\&alpha;})}{2}\right\}\end{array}\right]---\left(32\right)$

Under known track data code block T and channel parameter condition.Each circular correlation be respectively desirably in cycle frequency by different.Assuming that viewed sequence long enough, the phase place of stable circulation first peak is as follows

$\mathrm{\&phi;}=\mathrm{angle}\left\{\frac{1}{T}\underset{k=0}{\overset{T-1}{\mathrm{\&Sigma;}}}E\right\{g\left[y_i(2t-1)y_i\left(2t\right)\right]\}.\exp [-\frac{j2\mathrm{\&pi;t}}{T}\left]\right\}---\left(33\right)$

Wherein g [] represents that correlation function is classified by standard, and this phase place is decided by channel parameter.Such as, adopt Alamouti scheme, correlation function is y _i(2t-1) y _j(2t), during i ≠ j, the estimated value of phase place is φ=angle{H (1,1) H (2,2)-H (1,2) H (2,1) }.Cyclic Statistics is represented by following formula

${\mathrm{th}}_{\mathrm{ac}}=\underset{r=0}{\overset{R-1}{\mathrm{\&Sigma;}}}{\left|\exp (-j2{\mathrm{\&pi;\&phi;}}^r){\hat{C}}_{4Y}^r\left(\mathrm{\&alpha;}\right)\right|}^2---\left(34\right)$

In formula, R is the relative number of classifying by standard (29).

Can find out that Cyclic Statistics is at H ₀hypothesis under obey the degree of freedom be 2 card side distribution, at H ₁hypothesis under Normal Distribution.Therefore a given false alarm probability p _f(Probability of False Alarm), utilizes the character of card side's distribution to calculate threshold value γ

p _F＝p(χ ²＞γ) (35)

If th>=γ illustrates hypothesis H ₁set up, namely have employed STBC signal; Otherwise, otherwise H ₀set up, namely have employed BLAST signal.

According to above analysis, computer is next utilized to carry out simulating, verifying to algorithm.The actual conditions of emulation is as follows: consider synchronous MC-CDMA system up-link, mobile terminal two transmitting antenna M=2, base station single receive antenna, adopts Alamouti time block coding scheme and Blast signal, 16-QAM modulation system.Select orthogonal Walsh code as spreading code, sampling number is 5000 symbols.And same user's different antennae branch employs different spreading codes.If in emulation, channel is the gain turn down channels (L=2) such as two footpaths, the whose amplitude obeys rayleigh distributed in every bar footpath, phase place obey [0,2 π) between be uniformly distributed.

In order to reduce the impact of random noise, improving systematic function, improving discrimination, adopting data accumulation method when doing experiment simulation.Namely first data are divided into segment, are then averaging the Higher-Order Cyclic square of every section is cumulative.Quadravalence cyclic cumulants required after cumulative is like this than the better effects if not having cumulative stress release treatment of trying to achieve.Because the value that the curve of quadravalence cyclic cumulants only has carrier frequency to go out be perseverance just or permanent negative, and noise is change at random in time, is constant again, random noise can be cancelled out each other so cumulative after segmentation at same observation time intercarrier frequency.

Experiment 1 is when signal to noise ratio snr=0dB.Carry out the cyclostationarity analyzing STBC and BLAST two kinds of signals, data sampling frequency is 5.12kHz, produces 8 subcarriers, and subcarrier spacing is 50Hz.

Fig. 2 is the quadravalence cyclic cumulants of STBC and BLAST two kinds of signals.Can find out that quadravalence cycle frequency is not existed for BLAST code from Fig. 2 (a), 3 (b), and quadravalence cycle frequency is existed for STBC code.And as can be seen from Fig. 2 (a), when cycle frequency equals sub-carrier frequencies, subcarrier spacing is 50Hz, and sub-carrier number is 8, sub-carrier frequencies and the number of this STBC MC-CDMA signal therefore can be estimated.Fig. 2 (c) is the quadravalence cycle frequency of STBC code, employs correlation function as can be seen from Fig., there is not quadravalence cycle frequency in STBC code, different with Fig. 2 (a).The STBC code of Fig. 2 (a) have employed correlation function because be not that all correlation functions of STBC code have and there is this feature of quadravalence cycle frequency, so this standard having correlation function to select (29).It is fourth order cumulant secondary spectrogram in Fig. 2 (d).We carry out Quadratic Spectrum calculating with the one-dimension slice of the fourth order cumulant of signal, namely first ask its power spectral density, then remake leaf transformation in winning and delivery square, obtain the Quadratic Spectrum process of power spectrum signal.Width between these pulse trains is exactly the PN-code capture of signal.As can be seen from Fig., white Gaussian noise is suppressed.So, also can the PN-code capture T of detection signal under Low SNR _w.

Experiment 2 is at signal to noise ratio snr=[-20: 10] dB, during detection threshold γ=0.1, Progressive symmetric erythrokeratodermia algorithm performance is analyzed: under the conditions such as different data lengths, different channels environment, different emission rates, done algorithm performance by 150 Monte Carlo experiments compare.

Fig. 3 algorithm performance curve.As can be seen from Fig. 3 (a), channel quality has larger impact to discrimination, particularly when low signal-to-noise ratio.Sampling number is 5000 symbols, and do not know any other Parameter Conditions when only knowing data code block T under, recognition effect is poor, and as signal to noise ratio >=7dB, discrimination just reaches 100%.But, when under known track data code block T and channel parameter condition, improvement that recognition effect is obvious, particularly when low signal-to-noise ratio.As signal to noise ratio >=-5dB, discrimination all reaches more than 98%.Fig. 3 (b) and Fig. 3 (c) carry out algorithm performance under adopting different modulating mode situation for signal different length and signal respectively and compare.In Fig. 3 (b), sampling number is 5000,2500 and 1000 symbols, and algorithm performance is subject to the impact of sampled symbols number.As can be seen from Fig., sampled symbols number is more, and the detection for Space-Time Block Coding is more favourable, especially when low signal-to-noise ratio.Fig. 3 (c) carries out Performance comparision to adopting the signal of QPSK, 16QAM and 64QAM modulation system.Adopt the signal performance of QPSK modulation system much better, especially during signal to noise ratio≤-6dB.As signal to noise ratio >=-5dB, discrimination all reaches more than 99%, as signal to noise ratio >=-10dB, adopts the discrimination of the signal of QPSK modulation system to reach more than 90%.This just illustrates that algorithm performance also receives the impact of signal madulation mode.For STBC code but different rates has carried out algorithm performance compares in Fig. 3 (d).As can be seen from Fig., when adopting more better than employing 3/4 speed of the performance of full rate STBC code.Same can be generalized to arbitrary Space-Time Block Coding.Fig. 3 (e) is the Performance comparision that algorithm adopts different correlation function.Wherein Combined1 adopts correlation function , Combined2 adopts correlation function (y _i(2t-1) y _i(2t)), Combined3 adopts correlation function (y _i(2t-1) y _j(2t).As can be seen from Fig., when algorithm adopts different correlation function, algorithm performance is also different.Algorithm performance is when signal to noise ratio>=-5dB, and discrimination all reaches about 99%, wherein adopts correlation function (y _i(2t-1) y _j(2t) effect is best, especially when low signal-to-noise ratio.That DEM algorithm and EM algorithm performance compare in Fig. 3 (f).Along with the increase of signal to noise ratio, the performance of DEM algorithm is better than EM's.Further, the complexity of DEM algorithm is far smaller than the complexity of EM algorithm.Because DEM algorithm operates on D STBC MC-CDMA symbol, instead of phase EM algorithm operates on U planisphere is counted, so decrease computation complexity.The complexity of DEM algorithm is O (DK ²d ^k), the complexity of EM algorithm is O (DK ²u ^k), the complexity of LMS algorithm is O (DKU ^k), U is that planisphere is counted.

The foregoing is only of the present invention and be preferably not limited to the present invention, obviously, those skilled in the art can carry out various change and modification to the present invention and not depart from the spirit and scope of the present invention.Like this, if these amendments of the present invention and modification belong within the scope of the claims in the present invention and equivalent technologies thereof, then the present invention is also intended to comprise these change and modification.

Claims (1)

1. based on the Space-Time Block Coding MC-CDMA Signal blind recognition method of cyclostationarity, it is characterized in that, analyze based on the cyclostationarity of Space-Time Block Coding MC-CDMA signal, first set up the choice criteria of signal correction function, estimate the fourth order cumulant that these correlation functions are corresponding, then follow the parameter of channel to combine fourth order cumulant and set up a Cyclic Statistics, finally follow this Cyclic Statistics to compare according to the Detection and Extraction detection threshold of cycle frequency and do judgement realization identification; Concrete steps are as follows:

Step one: by signal Y (t) by T _ssampling formation time series, extract the code check of signal, obtain the correlation function number R of signal according to formula (29):

$\begin{array}{c}f\left(t\right)=E\left\{g\right[y_i(2t-1)y_j\left(2t\right)\left]\right\}\mathrm{orE}\left\{g{[y}_i(2t-1)y_j^{*}\left(2t\right)\right]\}\\ =f(t+\mathrm{lp})\end{array}$

(29)

T is the numbering of space-time code block, t=1,2 ..., LT, l are positive numbers, and f (t) is the function of period p, and g [] is a linear correlation function, definition $g[\&CenterDot;]=y_i(2t-1)y_i\left(2t\right)\mathrm{or}{y}_i(2t-1)y_j^{*}\left(2t\right),$ 0≤i, j ∈ I<M, I are set of integers;

Step 2: at cycle frequency α=± T/2T _s, the fourth-order cumulant value of respective signal is calculated according to formula (28)

${\hat{C}}_{4Y}(\mathrm{\&alpha;},\mathrm{\&tau;})=\frac{1}{N}\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}Y\left(n\right)Y^{*}(n+p)Y\left(n\right)Y^{*}(n+p).\exp (-\mathrm{j\&alpha;t})$ (28)；

Step 3: the phase estimating the stable circulation first peak of corresponding each correlation function according to formula (33) ^r

$\mathrm{\&phi;}=\mathrm{angle}\left\{\frac{1}{T}\underset{k=0}{\overset{T-1}{\mathrm{\&Sigma;}}}E\right\{g\left[y_i(2t-1)y_i\left(2t\right)\right]\}.\exp [-\frac{j2\mathrm{\&pi;t}}{T}\left]\right\}$ (33)；

Step 4: according to hypothesis detect with converging on zero-mean variance asymptotic is Σ _acthis character of multivariate normal distributions estimate a circle statistics value th _ac, adopt formula (31) or formula (34) to estimate:

${\mathrm{th}}_{\mathrm{ac}}=N\stackrel{^^}{c_{\mathrm{aY}}}(t;\mathrm{\&tau;}){\widehat{\mathrm{\&Sigma;}}}_{\mathrm{ac}}^{-1}{c}_{\mathrm{aY}}{(t;\mathrm{\&tau;})}^T$ (31)

In formula, N is data length, be the estimation of covariance matrix

${\mathrm{th}}_{\mathrm{ac}}=\underset{r=0}{\overset{R-1}{\mathrm{\&Sigma;}}}{\left|\exp (-j2\mathrm{\&pi;}{\mathrm{\&phi;}}^r){\hat{C}}_{4Y}^r\left(\mathrm{\&alpha;}\right)\right|}^2$ (34)

In formula, R is the relative number of classifying by formula (29);

Step 5: the formula (27) according to cycle frequency), obtain detection threshold value γ by formula (35)

$H_0:\mathrm{\&alpha;}\&NotElement;A_4,\&ForAll;{\left\{{\mathrm{\&tau;}}_n\right\}}_{n=1}^N\&DoubleRightArrow;{\hat{c}}_{4Y}(t;\mathrm{\&tau;})={\mathrm{\&epsiv;}}_{4Y}^T(\mathrm{\&alpha;};\mathrm{\&tau;})$

H ₁: $\mathrm{\&alpha;}\&NotElement;A_4,$ Exist (27)

$\&DoubleRightArrow;{\hat{c}}_{4Y}(t;\mathrm{\&tau;})=c_{4Y}(t;\mathrm{\&tau;})+{\mathrm{\&epsiv;}}_{4Y}^T(\mathrm{\&alpha;};\mathrm{\&tau;})$

Wherein A ₄it is the cycle frequency set of quadravalence cyclic cumulants;

p _F＝p(χ ²＞γ) (35)

P _fit is false alarm probability;

Step 6: compare judgement, if namely th>=γ illustrates hypothesis H ₁set up, namely have employed STBC signal; Otherwise, otherwise H ₀set up, namely have employed BLAST signal.